simplification Model Questions & Answers, Practice Test for ssc steno grade c d 2024
ssc steno grade c d 2024 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Power, Indices And Surds
Ratio & Proportion
Percentage
Time & Work
Time & Distance
Mensuration
One of the factors of the polynomial $x^4 – 7x^3 + 5x^2$ – 6x + 81 is:
Answer: (d)
Let f(x) = $x^4 – 7x^3 + 5x^2$ – 6x + 81
By hit and trial method,
$x^4 – 7x^3 + 5x^2$ – 6x + 81
= $x^3 (x – 3) – 4x^2(x – 3)$ – 7x(x – 3) – 27(x – 3)
= (x – 3) ($x^3 – 4x^2$ – 7x – 27)
(x – 3) is one of the factor of the given polynomial.
If , $a/b = b/c = c/d$ then which of the following is/are correct?
1. ${b^3 + c^3 + d^3}/{a^3 + b^3 + c^3} = d/a$
2.${a^2 + b^2 + c^2}/{b^2 + c^2 + d^2} = a/d$
Select the correct answer using the code given below.
Answer: (c)
Let $a/b = b/c = c/d$ = k
⇒a = bk, c = ck, c = dk
⇒abc = $bcdk^3$
⇒a = $dk^3$
(1) ${b^3 + c^3 + d^3}/{a^3 + b^3 + c^3} = d/a$
(2) ${a^2 + b^2 + c^2}/{b^2 + c^2 + d^2} = a/d$
⇒${b^3 + c^3 + d^3}/{b^3k^3 + c^3k^3 + d^3k^3} = d/a$
⇒${b^2k^2 + c^2k^2 + d^2k^2}/{b^2 + c^2 + d^2} = a/d$
⇒${b^3 + c^3 + d^3}/{(b^3 + c^3 + d^3)k^3} = d/a$
⇒${(b^2 + c^2 + d^2)k^2}/{b^2 + c^2 + a^2} = a/d$
⇒$1/{k^3} = d/a$
⇒$k^2 = a/d$
⇒$k^2 – k^3$
⇒$1/{a/d} = d/a$
which is not possible
⇒$d/a = d/a$
⇒only (1) is true.
∴ Option (a) is correct.
If ab + bc + ca = 0, then the value of ${(b^2 - ca) (c^2 - ab) + (a^2 - bc) (c^2 - ab) + (a^2 - bc) (b^2 - ca)}/{(a^2 - bc) (b^2 - ca) (c^2 - ab)}$
Answer: (a)
ab + bc + ca = 0
– ab = c(b + a).........(i)
– bc = a(b + c) .........(i)
– ca = b(a + c) .........(i)
ATQ,
${(b^2 - ca) (c^2 - ab) + (a^2 - bc) (c^2 - ab) + (a^2 - bc) (b^2 - ca)}/{(a^2 - bc) (b^2 - ca) (c^2 - ab)}$
$1/{a^2 - bc} + 1/{b^2 - ca} + 1/{c^2 - ab}$
$1/{a(a + b + c)} + 1/{b(a + b + c)} + 1/{c(a + b + c)}$
From (i)
${bc + ac + ab}/{(a + b + c) abc}$ = 0
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